Finding a globally optimal protocol to direct a stochastic evolution is a topic of control theory, known for its impact in engineering, economics and other fields [1]}. Here, we introduce a formalism based on optimal control to devise a population-level artificial selection strategy and drive the stochastic evolution of multi-variate molecular phenotypes towards a desired target. Importantly, we develop a framework to quantify how uncertainty and lack of evolutionary predictability can limit the efficacy of such artificial selection. By relating evolutionary predictability with control under artificial selection, we characterize how to best monitor a population and acquire a sufficient predictive information in order to optimally intervene with its evolution.
